I would try cleaning it myself . If u work on puters , and ur eyes are still good , give it a try.
I have 4 zs3's and a zs7 ....one of my zs3's has ur same problem when zoomed at something light colored ( like the sky ).
If u take it to a camera shop ur probably going to be spending more than the cameras worth.
BOB

I had the same problem with my zs8. So I tried extending and retracting the lens while holding a shop vac over the lens and that removed some of the spots. I had many many more than you did. After an exhaustive search on the internet I discovered that this was a fairly common problem with Panasonic point-and-shoots. I eventually gave up and now my camera sits on the shelf unused. Good luck with whatever decision you make. If you find a solution please reply to your post so the rest of us may get some relief haha

After trying the mobile phone trick (setting a vibrating mobile phone on the lens to hopefully knock the dust off, which did nothing) and doing an exhaustive and futile search on EBay for a comparable replacement, I took it to a highly regarded camera repair place in New York. They said it was definitely the sensor; it came to $70 including tax. I'll pick it up on Monday and will report back.

The problem I had with any of those available on EBay was that they all seemed pretty beat up. I always use those removable screen shields and in general take extremely good care of all of my cameras. Spending $175 for a beat up camera or paying $70 to fix mine seemed like a no-brainer.

The technician said this is a common problem that's easily resolved.

I really wasn't comfortable with the idea of trying to open it up myself.